Dr Tewari has developed computational resources with an expansible object-oriented framework in Java for handling exact coalescent recursions and doing Monte Carlo simulations with importance sampling. We have developed some general importance sampling strategies for speeding statistical algorithms for calculating coalescent probabilities. The strategies exploit the facility of exact probability calculation within the framework to increase the effective sample size by about four with negligible costs in computation time. Dr. Spouge has also developed some results relevant to inferring events at the initiation of viral infection, with potential applications to, e.g., trials of HIV vaccines and preventative therapies.